{ \left( { C }_{ n } \right) }^{ 12 } = { \left( { C }_{ n } \right) }^{ 8 } { \left( { C }_{ n } \right) }^{ 19 } = { \left( { A }_{ x } \right) }^{ 2 }
Solve for C_n
\left\{\begin{matrix}C_{n}=0\text{, }&A_{x}=0\\C_{n}=1\text{, }&|A_{x}|=1\end{matrix}\right.
Solve for A_x
\left\{\begin{matrix}A_{x}=0\text{, }&C_{n}=0\\A_{x}=-1\text{; }A_{x}=1\text{, }&C_{n}=1\end{matrix}\right.
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